Soil Compressibility Model

Three models are available in PFLOTRAN to compute the soil compressibility, which reflect sthe rock porosity changes due to pressure build ups and relaxations. The use of ‘soil’ rather than ‘rock’ reflects PFLOTRAN’s general-purpose origins, but they are applied to the pore volume of the rock. The available models are Leijnse, BRAGFLO and a quadratic model.

These formulations are described below:

The Leijnse soil compressibility model

(1)\[\phi_{\mbox{eff}} = 1−(1−\phi_0 ) \exp\left[ −C_{\mbox{rock}} ( p− p_{\mbox{ref}} ) \right]\]

where:

\[\begin{split}\begin{split} &p &= \mbox{pressure [Pa]} \\ &p_{\mbox{ref}} &= \mbox{reference pressure [Pa]} \\ &\phi_{\mbox{eff}} &= \mbox{effective porosity [-]} \\ &\phi_0 &= \mbox{initial (unperturbed) porosity [-]} \\ &C_{\mbox{rock}} &= \mbox{rock compressibility [1/Pa]} \\ \end{split}\end{split}\]

The BRAGFLO soil compressibility model

(2)\[\phi_{\mbox{eff}} = \phi_0 \exp\left[C_{\mbox{rock}} ( p− p_{\mbox{ref}} ) \right]\]
\[\begin{split}\begin{split} &p &= \mbox{pressure [Pa]} \\ &p_{\mbox{ref}} &= \mbox{reference pressure [Pa]} \\ &\phi_{\mbox{eff}} &= \mbox{effective porosity [-]} \\ &\phi_0 &= \mbox{initial (unperturbed) porosity [-]} \\ &C_{\mbox{rock}} &= \mbox{rock compressibility [1/Pa]} \\ \end{split}\end{split}\]

The Quadratic soil compressibility model

(3)\[\Phi = \Phi( P_{\mbox{ref}} ) \left( 1 + X + \frac{X^2}{2} \right),\]

where:

\[\begin{split}\begin{split} &X &= C_{\mbox{rock}} ( P−P_{\mbox{ref}} ) \\ &\Phi &= \mbox{porosity} \\ &P &= \mbox{pressure [Pa]} \\ &P_{\mbox{ref}} &= \mbox{reference pressure [Pa]} \\ &C_{\mbox{rock}} &= \mbox{rock compressibility [1/Pa]} \\ \end{split}\end{split}\]